Dynamical evolution of the chiral magnetic effect: Applications to the quark-gluon plasma

TL;DR

This paper investigates the time-dependent behavior of the chiral magnetic effect in conducting media, especially in quark-gluon plasma, revealing how magnetic helicity and fermion imbalance evolve and transfer energy under different initial conditions.

Contribution

It derives the dynamical evolution equations from chiral kinetic theory and applies them to model the chiral magnetic effect in quark-gluon plasma, highlighting the helicity transfer mechanisms.

Findings

Helicity transfer depends on initial conditions and wavelength scales.

Chiral fermion imbalance influences magnetic field dynamics.

Magnetic helicity and fermion density are interconnected through quantum conservation laws.

Abstract

We study the dynamical evolution of the so-called chiral magnetic effect in an electromagnetic conductor. To this end, we consider the coupled set of corresponding Maxwell and chiral anomaly equations, and we prove that these can be derived from chiral kinetic theory. After integrating the chiral anomaly equation over space in a closed volume, it leads to a quantum conservation law of the total helicity of the system. A change in the magnetic helicity density comes together with a modification of the chiral fermion density. We study in Fourier space the coupled set of anomalous equations and we obtain the dynamical evolution of the magnetic fields, magnetic helicity density, and chiral fermion imbalance. Depending on the initial conditions we observe how the helicity might be transferred from the fermions to the magnetic fields, or vice versa, and find that the rate of this transfer also depends on the scale of wavelengths of the gauge fields in consideration. We then focus our attention on the quark-gluon plasma phase, and analyze the dynamical evolution of the chiral magnetic effect in a very simple toy model. We conclude that an existing chiral fermion imbalance in peripheral heavy ion collisions would affect the magnetic field dynamics, and consequently, the charge dependent correlations measured in these experiments.